The present invention relates to a target shape generating and/or displaying process. The term xe2x80x9cthe generating process of a shapexe2x80x9d used here means a generating process of a general shape, including a synthesizing and decomposing process of a shape, and moreover an embedding process of a target shape in the world of shapes by means of an integrating activity. The term xe2x80x9cthe displaying process of a shapexe2x80x9d means a displaying process of the results of the above process, for example, the shape generating process. The general shape refers to a 3D and/or 2D shape. The 3D shape contains polyhedrons, curved surface bodies and compound shape bodies thereof, etc.; and the 2D shape contains polygons, curves and compound type shapes thereof, etc.
FIG. 8 shows a winged edge structure which is well-known and considered to be a supporting technology for shape modeling in the conventional shape forming process. It is clear from this Figure that the winged edge structure carries out the handling process of an applied shape by developing shape state information based on the edge of the target shape, in other words, the ridge of the target shape constructed between vertices of the shape. In the above case, the target shape is fundamentally represented as a polyhedron. Thus, the power of the winged edge structure independently corresponds to the processing of the line state shape, and it also relates to a line-like displaying image.
In the conventional example described above, it is necessary to embed the function which expresses the curved surface when the curved surface is processed. Based on the function which is embedded by pointers, data of the curved surface are created; and the process which develops such data on a basic polyhedron regarded as a maternal body of a target shape is also required. In other words, in the winged edge structure, it is necessary to add an additive mechanism for processing the curved surface to a basic polyhedron structure.
Thus, the conventional winged edge structure is inefficient with respect to a shape processing such as a shape generating and displaying process, because the double interface for both the curved surface body and polyhedron must be set, and there are so many problems that they cannot be done so as to comply with the object, etc. As a result, the efficient construction of the shape database, etc. is made more difficult. In addition, in the dynamic (time-varying) image process, etc., the efficient process cannot be desired, and the dynamic management on the shape processing for the bi-direction game, etc. cannot be almost expected.
The winged edge structure involves another large problem in addition to the problem described above. It is a problem that a direct management of configuration information on assembling information is almost impossible. One of the solutions of the problem is a practical method that was established as a more practical method shown in FIG. 9. In the case of this solution, the movement of the target shape is used as operational information for the shape assembling. Even in this case, a free and efficient shape processing cannot be expected because there is a problem that the degree of freedom of the operation is low for the shape handling process which composes the target shape from the shape part, etc.
The objective of the present invention is to provide an efficient and convenient method that can establish an integrating and unification process of a polyhedron and curved surface bodies and other general shape bodies, thus solving the problems of prior art methods.
The present invention relates to a processing of a plane-like image which is mainly comprised of triangles in the field of a generating and/or displaying process of general shapes including polyhedron, curved surface bodies, and compound and/or complex bodies thereof. Fundamentally, the plane-like image processing means a displaying process of a 3D shape. In the present invention, for example, complex bodies are constructed by directly embedding a curved surface structure in a polyhedron structure; and with this embedding structure, the general shape processing is realized as a consistent and unified process.
More specifically, the general shape is expressed by assembling several parts of shapes, and the whole shape is hierarchically constructed. Each of the parts of shapes is constructed based on the shape forming unit of a triangle. This shape forming unit is called FACET. FACET is a hyperplane cut off as a planar state shape, for example, a triangular shape. The hyperplane as a 3D shape is the plane which bisects the space. In this meaning, the hyperplane in 3D space is a plane constructed by shape composing points and an azimuth vector on this composing point, namely, a plane with a normal line, which is called a tangent plane in the case of a curved surface.
A curved surface on a maternal body is formed as a hierarchical configuration of FACET (a FACET assembly), which is already defined as a shape forming unit. This is an embedding structure or a nesting structure on the maternal body surface, thus constructing an integrating structure for a shape handling process and providing a structuring and organizing function which can realize a unified process.
Geometric information is constructed based upon orienting information (the normal vector and/or tangent vector) on the shape composing point and positioning information (coordinate point) of this composing point.
In this meaning, information of planar state shapes is equal to information of FACET, and then the whole shape is constructed as a hierarchical structure of FACET information. This species of hierarchical structures can be theoretically applied for the unstructuring shape modeling but practically functions efficiently and effectively for the structuring shape modeling. In this case, structured planar state shape information is made up as composing information of FACET of the triangle. In other words, it is isomorphically constructed based on a set of three pieces of geometric information. With this frame, it is possible to construct fully and completely the above species of structures.
Information on an upper side hierarchical structure, namely, a super-structure, should be called assembling information, and a frame-work of a super-structure related to assembling information is systematically built up as the function of composing information that shows a constructive relationship of the hierarchy.
Operational information that functions as assembling information is constituted by a combination of both positioning information (a movement of the coordinate) and information of the azimuth of the relative coordinate (a rotation of the coordinate axis), wherein a movement of the coordinate is related to the center of a shape part, which shows the relationship between the absolute coordinate and the relative coordinate respectively used for the physical world and the display world as the setting coordinate, and a rotation of the coordinate axis is related to the display coordinate of objects. This information serves as management information of the target shape, and moreover performs one role of geometric information, which directly works for the target shape.
Main assembling information is constructed based on connecting information which functions as mutual linkage information of the hierarchical structure. Not only the role of connecting information which shows the unambiguous hierarchical relationship but also the role of freely and efficiently realizing the shape processing are performed. Accordingly, this species of connecting information is called a direct identifier of the hierarchical structure.
As a complementary role of connecting information, an indirect identifier of the hierarchical structure is set up. The indirect identifier of the hierarchical structure mutually and freely regulates the relationship among parts of shapes. By way of using this identifier, the shape processing is efficiently carried out because historical management of parts, etc. can be freely realized.
By means of the modified tetra decimal number system method, that is a modified method of remainder calculation with 4n(mod 4) and/or exponential calculation with 4n (the n-th power of 4), the management of the curved surface is realized based on the structuring and organizing function as a type of FACET from a native property. Accordingly, the modeling accuracy of the target shape, etc. can be freely controlled.
As seen from the above, an upper side managing and/or controlling structure, that is defined above as a super-structure, by the systematic hierarchical organization of assembling information and a lower side controlling structure, namely, a last-structure, by the systematic hierarchical organization of geometric information are constructed. By systematically controlling the organized structure related as above, the generating and/or displaying process of polyhedrons, curved surface bodies, various shapes such as complex bodies and the world of shape and image is carried out as an integrating and/or unification process for the shape and image.